23 June 2010

The ridiculously long match at Wimbledon

As you may have heard, there's a match at Wimbledon , between John Isner and Nicolas Mahut, in which the last set is tied at 59 games. (The previous longest set at Wimbledon was 24-22.)

A set goes until one player has won six games, and has also won two more than the opponent. This means that back since the set was tied at 5 games, games 11 and 12 were split by the two players; so were 13 and 14; and so on up to 117 and 118.

Terence Tao points out that this is very unlikely using a reasonable naive model of tennis, which assumes that the player serving has a fixed probability of winning the game. (Service alternates between games.) His guess is that some other factor is at play; for example, "both players may perform markedly better when they are behind".

This seems statistically checkable, at least if records of that sort of thing are kept. I'm not sure if they are; it seems like tennis scores are often reported as just the number of games won by each player in each set, not their order. Another hypothesis, of course, is that the match has taken on a life of its own and, subconsciously, the players are playing to keep the pattern going.

Both Isner and Mahut have excellent serves. After the first 20 games of the 5th set, they must both be so exhausted that neither had the energy to return each other's serves. This could partially explain why they kept on holding service games. I saw parts of the game: there were no rallies; almost all points ended in 3 shots or less by the 100th game or so.